If you say you are of the same religion as a bigot, you're telling the bigots that you agree with them, even if you don't.
Hitler and I may have agreed that the sky is blue, but if someone uses this to say we agree in general, they are simply being unreasonable. There are countless denominations of Christianity as a result of people disagreeing with each other about history and values. The Christian label is not synonymous with bigotry, and we could use more counterexamples if people seem to think otherwise.